1) Introduction
From video games and engineering to movies and the arts, vectors are powerful mathematical tools that can be found just about everywhere. In this session, we will explore what vectors are and how they relate to the physical world and the study of physics.
Some measurable quantities in our world only indicate how much of something there is such as mass, temperature, or speed. These are called Scalar values.
Thought Question 1.1: What other scalar values can you think of?
"Sorry officer, how fast was I going?"
"100 mph"
Other measurements combine quantity with a specific direction and these are called Vectors .
"I guess I was going 100 mph, but at least I was going 100 mph southbound with traffic."
By specifying the direction of movement, we have taken the scalar speed value and created the Vector quantity velocity. Position, velocity, and acceleration are all vectors representing your current state in the physical world.
Vectors can be added, subtracted, and even scaled. One quick way to visualize these operations Vector is to think of yourself on a city grid map. If you walk 2 mph north and then immediately turn around and walk two mph south over the same amount of time, you will return to your original location. This is a simple form of vector addition.
Thought Question 1.3: Where would you wind up if you ran 4mph north and then immediately turned around and walked two mph south?
We can also use vectors to find out how far we have walked if we walk 2 mph north and then immediately 2 mph east. This is called finding the length or magnitude of a vector .
As we progress through this unit, we will see how vectors can be used to decompose the flight of projectiles into two separate vector components situated along two major axis - up/down and right/left - and make problem solving much easier.
2) Review Before we begin, let's review some of the equations of motion and situate them in a one-dimensional world.
Thought Question 1.4: What are the variables in these equations? Can you rephrase these equations in your own words?
Review Question 1.1: If a Toyota starts at rest and suddenly accelerates to 4 m/s², how far will it travel in 5 seconds? Why?
3) New Content and Assignment
5. Vectors - Physics must explain not only why and how much, but also where and which way.
Mechanical Universe - Vectors
Thought Question 1.6: What other vector quantities can you think of?
Plane and wind example http://www.physicsclassroom.com/mmedia/vectors/plane.cfm
Review Question 1.2:How do airlines estimate how long your flight time will be? Thought Question 1.5: Given the same plane, why does it take longer to fly west bound than to fly east bound on roundtrips?
4) Assignment Submission
Comparison of graphical and numerical vector solutions
Students will need to pair up to solve a set of vector addition and subtraction problems by using both graphical and numerical means.
If you have a graphical problem, you will have to:
Solve your problem graphically using this applet :
Post a screenshot of your solution to this docs page :
If you have a numerical problem, you will have to:
Solve your problem using numerical means
Find the complimentary screen shot of the graphical solution that matches yours.
Once you have located your counterpart, type your name underneath the image.
Here is the list of possible vectors:
1
2
3
4
5
6
7
8
9
10
A
<3,3>
<4,4>
<1,1>
<5,0>
<0,-7>
<0,0>
<3,5>
<-1.-1>
<5,0>
<0,5>
B
<4,3>
<1,3>
<6,0>
<-5,0>
<0,7>
< 7,9>
< 3,3>
< 2,2>
<0,5>
<-5,0>
Find out if you are going to be finding numerical or graphical solutions for each pair of vectors by accessing your Personalized Student Data at zoho .
Take a quiz to see what you know
Teacher Crafted Activity 1.x : [ content can be added through a teacher admin interface ]
5) Personal Learning Log Contributions As we do at the end of each session, we will contribute a summary of what we have learned in our own words, images, and links to our personal course review log. The purpose of which is to evolve a review book for the entire course.
Additionally, each of you will submit three unique questions and answers based on the content learned this session, Make them fun and challenging for your classmates. We will vote on the best ones, so be creative!
Week 1 - Vectors
1) Introduction
From video games and engineering to movies and the arts, vectors are powerful mathematical tools that can be found just about everywhere. In this session, we will explore what vectors are and how they relate to the physical world and the study of physics.
Some measurable quantities in our world only indicate how much of something there is such as mass, temperature, or speed. These are called Scalar values.
Thought Question 1.1: What other scalar values can you think of?
"Sorry officer, how fast was I going?"
"100 mph"
Other measurements combine quantity with a specific direction and these are called Vectors .
"I guess I was going 100 mph, but at least I was going 100 mph southbound with traffic."
By specifying the direction of movement, we have taken the scalar speed value and created the Vector quantity velocity. Position, velocity, and acceleration are all vectors representing your current state in the physical world.
Vectors can be added, subtracted, and even scaled. One quick way to visualize these operations Vector is to think of yourself on a city grid map. If you walk 2 mph north and then immediately turn around and walk two mph south over the same amount of time, you will return to your original location. This is a simple form of vector addition.
Thought Question 1.3: Where would you wind up if you ran 4mph north and then immediately turned around and walked two mph south?
We can also use vectors to find out how far we have walked if we walk 2 mph north and then immediately 2 mph east. This is called finding the length or magnitude of a vector .
As we progress through this unit, we will see how vectors can be used to decompose the flight of projectiles into two separate vector components situated along two major axis - up/down and right/left - and make problem solving much easier.
2) Review
Before we begin, let's review some of the equations of motion and situate them in a one-dimensional world.
Thought Question 1.4: What are the variables in these equations? Can you rephrase these equations in your own words?
Review Question 1.1: If a Toyota starts at rest and suddenly accelerates to 4 m/s², how far will it travel in 5 seconds? Why?
3) New Content and Assignment
5. Vectors - Physics must explain not only why and how much, but also where and which way.
Thought Question 1.6: What other vector quantities can you think of?
Reading
Vectors
Interactive Examples
River crossing example
http://www.physicsclassroom.com/mmedia/vectors/rb.cfm
Thought Question 1.4: In this example, which boat is likely to reach the other shore first? Why?
http://www.physicsclassroom.com/shwave/rboat.cfm
Plane and wind example
http://www.physicsclassroom.com/mmedia/vectors/plane.cfm
Review Question 1.2: How do airlines estimate how long your flight time will be?
Thought Question 1.5: Given the same plane, why does it take longer to fly west bound than to fly east bound on roundtrips?
Vector addition and subtraction example
http://www.frontiernet.net/~imaging/vector_calculator.html
Thought Question 1.6: Calculating the magnitude of a vector looks an awful like using what geometric triangular relationship?
4) Assignment Submission
Comparison of graphical and numerical vector solutions
Students will need to pair up to solve a set of vector addition and subtraction problems by using both graphical and numerical means.
If you have a graphical problem, you will have to:
If you have a numerical problem, you will have to:
Once you have located your counterpart, type your name underneath the image.
Here is the list of possible vectors:
Take a quiz to see what you know
Teacher Crafted Activity 1.x : [ content can be added through a teacher admin interface ]
5) Personal Learning Log Contributions
As we do at the end of each session, we will contribute a summary of what we have learned in our own words, images, and links to our personal course review log. The purpose of which is to evolve a review book for the entire course.
Additionally, each of you will submit three unique questions and answers based on the content learned this session, Make them fun and challenging for your classmates. We will vote on the best ones, so be creative!